Learn Italian: Non ho mai mangiato ciliegie così buone. - I have never eaten such good cherries.

The singular noun is ciliegia. The rule for feminine nouns ending in unstressed -cia and -gia depends on the letter that comes right before it. If the letter before is a vowel (like the 'e' in ciliegia), the 'i' is kept in the plural. If it is a consonant (like in pioggia -> piogge), the 'i' is dropped.

Ciliegie is feminine plural, so why is the past participle mangiato instead of mangiate?

In Italian, when a verb uses the auxiliary avere (like ho here), the past participle usually stays in its default -o form. It would only change to match the object if you used a direct object pronoun before the verb, like le ho mangiate (I have eaten them).

The English translation says "such good cherries", but isn't così the word for "so"?

Yes, così generally translates to "so". Italian doesn't have a direct structural equivalent for the English phrase "such [adjective] [noun]". Instead, Italians word it as "[noun] so [adjective]"—in this case, ciliegie così buone (literally, "cherries so good").

Why is mai placed directly between ho and mangiato?